Let ( (z) be an entire function that is represented by a series of the form

(a) By differentiating the composite function g(z) = ([( (z)] successively, find the first three nonzero terms in the Maclaurin series for g(z) and thus show that

(b) Obtain the result in part (a) in a formal manner by writing

Replacing f (z) on the right-hand side here by its series representation, and then collecting terms in like powers of z.
(c) By applying the result in part (a) to the function f (z) = sin z, show that

Transcribed Image Text:

sinsin z) = z--z3 + (に1 <00).